Lesson Notes By Weeks and Term v4 - SHS 1
MEASUREMENT OF TRIANGLES
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MEASUREMENT OF TRIANGLES
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 8
Grade code: 1.2.2.LI.4
Strand code: 2
Sub-strand code: 2
Content standard code: 1.2.2.CS.1
Indicator code: 1.2.2.LI.4
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: MEASUREMENT OF TRIANGLES
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This lesson extends our understanding of trigonometry beyond the familiar SOH CAH TOA of right-angled triangles. We will introduce the unit circle, a powerful tool that allows us to find trigonometric values for *any* angle, not just acute ones. Specifically, we will focus on quadrantal angles (0°, 90°, 180°, 270°, 360°), which form the fundamental reference points for all other angles. This concept is crucial in fields like physics (describing waves from the Akosombo Dam), engineering (designing structures like the Adomi Bridge), and navigation on the Volta Lake.
This section breaks down the core ideas needed to master this topic. We will build our knowledge step-by-step. Part 1: The Unit Circle
The unit circle is a circle drawn on the Cartesian plane (the x-y graph) with two special properties: Its center is at the origin, point (0, 0). Its radius is exactly 1 unit. Why is it useful? Because the radius is 1, it simplifies our trigonometric definitions. Part 2: Angles in Standard Position
An angle is in "standard position" when: Its vertex is at the origin (0, 0). Its initial side lies along the positive x-axis. Its terminal side is where the angle ends after rotation.
Rotation is measured: Anti-clockwise for positive angles (e.g., 90°). Clockwise for negative angles (e.g., -90°). Part 3: Redefining Trig Ratios on the Unit Circle